DOCSLIB.ORG

The Meissner Effect

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
The Meissner Effect The Meissner Effect When a material makes the transition from the normal to superconducting state, it actively excludes magnetic fields from its interior; this is called the Meissner effect. This constraint to zero magnetic field inside a superconductor is distinct from the perfect diamagnetism which would arise from its zero electrical resistance. Zero resistance would imply that if you tried to magnetize a superconductor, current loops would be generated to exactly cancel the imposed field (Lenz's law). But if the material already had a steady magnetic field through it when it was cooled trough the superconducting transition, the magnetic field would be expected to remain. If there were no change in the applied magnetic field, there would be no generated voltage (Faraday's law) to drive currents, even in a perfect conductor. Hence the active exclusion of magnetic field must be considered to be an effect distinct from just zero resistance. A mixed state Meissner effect occurs with Type II materials. One of the theoretical explanations of the Meissner effect comes from the London equation. It shows that the magnetic field decays exponentially inside the superconductor over a distance of 20-40 nm. It is described in terms of a parameter called the London penetration depth. Perfect Diamagnet Superconductor If a conductor already had a steady Remarkably, the magnetic behavior of a magnetic field through it and was then superconductor is distinct from perfect cooled through the transition to a zero diamagnetism. It will actively exclude any resistance state, becoming a perfect magnetic field present when it makes the diamagnet, the magnetic field would be phase change to the superconducting state. expected to stay the same. 1 Magnetic Levitation Magnetic fields are actively excluded from superconductors (Meissner effect). If a small magnet is brought near a superconductor, it will be repelled becaused induced supercurrents will produce mirror images of each pole. If a small permanent magnet is placed above a superconductor, it can be levitated by this repulsive force. The black ceramic material in the illustrations is a sample of the yttrium based superconductor. By tapping with a sharp instrument, the suspended magnet can be caused to oscillate or rotate. This motion is found to be damped, and will come to rest in a few seconds. Levitation Currents The Meissner effect in superconductors like this black ceramic yttrium based superconductor acts to exclude magnetic fields from the material. Since the electrical resistance is zero, supercurrents are generated in the material to exclude the magnetic fields from a magnet brought near it. The currents which cancel the external field produce magnetic poles which mirror the poles of the permanent magnet, repelling them to provide the lift to levitate the magnet. The levitation process is quite remarkable. Since the levitating currents in the superconductor meet no resistance, they can adjust almost instantly to maintain the levitation. The suspended magnet can be moved, put into oscillation, or even spun rapidly and the levitation currents will adjust to keep it in suspension. 2 Quantum Superconducting Effects Although many properties of superconductors can be described in macroscopic terms such as resistivity, heat capacity, critical temperature, etc., superconductivity is at base a quantum phenomenon and several interesting quantum effects arise. In 1961, two groups working independently discovered flux quantization - the fact that the magnetic flux through a superconducting ring is an integer multiple of a flux quantum. The Cooper pairs of a superconductor can tunnel through a thin insulating layer between two superconductors. This is the basis for the Josephson junction which is used in high-speed switching devices. Flux Quantization Deaver and Fairbank did experiments with a tiny superconducting cylinder made by electroplating tin on a copper wire. They found magnetic flux quantized in units of such that the flux through the cylinder was given by 3 Type I Superconductors The 27 pure metals listed in the table below are called Type I superconductors. The identifying characteristics are zero electrical resistivity below a critical temperature, zero internal magnetic field (Meissner effect), and a critical magnetic field above which superconductivity ceases. Tc Mat. (K) Tc Rh 0 Mat. (K) W 0.015 The superconductivity in Type I superconductors is modeled well Gd* 1.1 Be** 0.026 by the BCS theory which relies upon electron pairs coupled by Al 1.2 lattice vibration interactions. Remarkably, the best conductors at Ir 0.1 Pa 1.4 room temperature (gold, silver, and copper) do not become Lu 0.1 superconducting at all. They have the smallest lattice vibrations, Th 1.4 so their behavior correlates well with the BCS Theory. Hf 0.1 Re 1.4 Ru 0.5 While instructive for understanding superconductivity, the Type I Tl 2.39 Os 0.7 superconductors have been of limited practical usefulness In 3.408 because the critical magnetic fields are so small and the Mo 0.92 superconducting state disappears suddenly at that temperature. Sn 3.722 Zr 0.546 Type I superconductors are sometimes called "soft" Hg 4.153 superconductors while the Type II are "hard", maintaining the Cd 0.56 superconducting state to higher temperatures and magnetic fields. Ta 4.47 U 0.2 La 6.00 Ti 0.39 Pb 7.193 Zn 0.85 Ga 1.083 *Gd at Tc=1.1 is questionable. Source is Rohlf, Ch 15, but this may be a misprint. Ga has Tc about 1.1, so Ga value may have been attributed to Gd. **"Superconductivity of Hexagonal Beryllium'" R.L. Falge Jr., Physics Letters A 24 1967. Mat. Tc Note also the three metals at right which were formerly included as Type I V 5.38 superconductors in the above table, but have been shown to exhibit Type II properties. Tc 7.77 Nb 9.46 4 Type II Superconductors Superconductors made from alloys are called Type II superconductors. Besides being mechanically harder than Type I superconductors, they exhibit much higher critical magnetic fields. Type II superconductors such as niobium- titanium (NbTi) are used in the construction of high field superconducting magnets. Type-II superconductors usually exist in a mixed state of normal and superconducting regions. This is sometimes called a vortex state, because vortices of superconducting currents surround filaments or cores of normal material. Magnesium Diboride In March 2001, Jun Akimitsu and colleagues at Aoyama-Gakuin University in Tokyo, Japan reported a superconducting transition temperature of 39 Kelvin for magnesium diboride. This has generated a great deal of excitement not only because this is the highest transition temperature yet observed for a type-II superconductor, but also because the materials used are quite common. There will be a great deal of interest in whether the material can be used to form wires. If its mechanical properties can be managed, it could contribute significantly to making superconducting magnets. Sergey L. Bud'ko and colleagues at Iowa State University have formed wires from the material. They observed the isotope effect in this superconductor, suggesting that it follows the behavior of other conventional superconductors. The isotope effect is a signature of interaction with the crystal lattice via phonons, and is an indication that the superconductor may act according to the BCS theory of superconductivity. All of this is preliminary information. Part of it was drawn from: "Run-of-the-mill compound becomes superstar" by P. Weiss, Science News 159, p134 (Mar 3, 2001) Superconducting Plutonium The plutonium compound PuCoGa5 has been found to be superconducting with a critical temperature of about 18 K. Gregory Stewart of the University of Florida and John Sarrao and colleagues at the Los Alamos National Laboratory reported this unexpected superconductor in the journal Nature. 5 .
Load more

Recommended publications
  • Lecture Notes: BCS Theory of Superconductivity
    Lecture Notes: BCS theory of superconductivity Prof. Rafael M. Fernandes Here we will discuss a new ground state of the interacting electron gas: the superconducting state. In this macroscopic quantum state, the electrons form coherent bound states called Cooper pairs, which dramatically change the macroscopic properties of the system, giving rise to perfect conductivity and perfect diamagnetism. We will mostly focus on conventional superconductors, where the Cooper pairs originate from a small attractive electron-electron interaction mediated by phonons. However, in the so- called unconventional superconductors - a topic of intense research in current solid state physics - the pairing can originate even from purely repulsive interactions. 1 Phenomenology Superconductivity was discovered by Kamerlingh-Onnes in 1911, when he was studying the transport properties of Hg (mercury) at low temperatures. He found that below the liquifying temperature of helium, at around 4:2 K, the resistivity of Hg would suddenly drop to zero. Although at the time there was not a well established model for the low-temperature behavior of transport in metals, the result was quite surprising, as the expectations were that the resistivity would either go to zero or diverge at T = 0, but not vanish at a finite temperature. In a metal the resistivity at low temperatures has a constant contribution from impurity scattering, a T 2 contribution from electron-electron scattering, and a T 5 contribution from phonon scattering. Thus, the vanishing of the resistivity at low temperatures is a clear indication of a new ground state. Another key property of the superconductor was discovered in 1933 by Meissner.
    [Show full text]
  • Superconductivity: the Meissner Effect, Persistent Currents and the Josephson Effects
    Superconductivity: The Meissner Effect, Persistent Currents and the Josephson Effects MIT Department of Physics (Dated: March 1, 2019) Several phenomena associated with superconductivity are observed in three experiments carried out in a liquid helium cryostat. The transition to the superconducting state of several bulk samples of Type I and II superconductors is observed in measurements of the exclusion of magnetic field (the Meisner effect) as the temperature is gradually reduced by the flow of cold gas from boiling helium. The persistence of a current induced in a superconducting cylinder of lead is demonstrated by measurements of its magnetic field over a period of a day. The tunneling of Cooper pairs through an insulating junction between two superconductors (the DC Josephson effect) is demonstrated, and the magnitude of the fluxoid is measured by observation of the effect of a magnetic field on the Josephson current. 1. PREPARATORY QUESTIONS 0.5 inches of Hg. This permits the vaporized helium gas to escape and prevents a counterflow of air into the neck. Please visit the Superconductivity chapter on the 8.14x When the plug is removed, air flows downstream into the website at mitx.mit.edu to review the background ma- neck where it freezes solid. You will have to remove the terial for this experiment. Answer all questions found in plug for measurements of the helium level and for in- the chapter. Work out the solutions in your laboratory serting probes for the experiment, and it is important notebook; submit your answers on the web site. that the duration of this open condition be mini- mized.
    [Show full text]
  • A Classical Deviation of the Meissner Effect in a Classical Textbook
    A Purely Classical Derivation of the Meissner Effect? A.M. Gulian∗ (Advanced Physics Laboratory, Chapman University, 15202 Dino Dr., Burtonsville, MD 20861, USA) Abstract.— A recent study (arXiv:1109.1968v2, to be published in American Journal of Physics) claims to provide a classical explanation of the Meissner effect. However, the argument misuses de Gennes’ derivation of flux expulsion in superconductors. In a recent publication [1], Essén and Fiolhais attempt to explain the Meissner effect in superconductors in a “purely classical” way. They utilize many arguments, most of which we will ignore in this short remark. Rather, we address their most crucial argument based on the excerpts from de Gennes’ classical textbook [2]. Following de Gennes, Ref. 1 writes the supercurrent density as j(r) = n(r)ev(r) , (1) where n is the density of superconducting electrons. In Ref. 1, they label v as the electron velocity, whereas De Gennes explicitly declares it to be carriers drift1 velocity. Substituting this equation into the expression for kinetic energy 1 E = n(r)mv 2 (r)dV , (2) k ∫ 2 subject to ∇ × h = (4π / c) j , and minimizing the sum of kinetic and magnetic energy E = (h2 /8π )dV mag ∫ with respect to the configuration of local magnetic field h, one can arrive at the F. and H. Londons’ equation: Submitted 1/29/2012 h + λ2∇ × (∇ × h) = 0 (3) where λ is the penetration depth. Equation (3), of course, explains the field repulsion. Based on this, and also noticing that the derivation of Eq. (3) “utilizes no quantum concepts and contains no Planck constant,” Essén and Fiolhais eventually deduce that superconductors “are just perfect conductors.” De Gennes himself never drew this conclusion.
    [Show full text]
  • The Physics and Applications of Superconducting Metamaterials
    The Physics and Applications of Superconducting Metamaterials Steven M. Anlage1,2 1Center for Nanophysics and Advanced Materials, Physics Department, University of Maryland, College Park, MD 20742-4111 2Department of Electrical and Computer Engineering, University of Maryland, College Park, MD 20742 We summarize progress in the development and application of metamaterial structures utilizing superconducting elements. After a brief review of the salient features of superconductivity, the advantages of superconducting metamaterials over their normal metal counterparts are discussed. We then present the unique electromagnetic properties of superconductors and discuss their use in both proposed and demonstrated metamaterial structures. Finally we discuss novel applications enabled by superconducting metamaterials, and then mention a few possible directions for future research. speculates about future directions for these Our objective is to give a basic metamaterials. introduction to the emerging field of superconducting metamaterials. The I. Superconductivity discussion will focus on the RF, microwave, Superconductivity is characterized by and low-THz frequency range, because only three hallmark properties, these being zero DC there can the unique properties of resistance, a fully diamagnetic Meissner effect, superconductors be utilized. Superconductors and macroscopic quantum phenomena.1,2,3 have a number of electromagnetic properties The zero DC resistance hallmark was first not shared by normal metals, and these discovered by Kamerlingh Onnes in 1911, and properties can be exploited to make nearly has since led to many important applications ideal and novel metamaterial structures. In of superconductors in power transmission and section I. we begin with a brief overview of energy storage. The second hallmark is a the properties of superconductors that are of spontaneous and essentially complete relevance to this discussion.
    [Show full text]
  • 14.4. the Ginzburg–Landau Theory the BCS Theory Answered the Question Why Electrons Pair Up
    Phys520.nb 119 This is indeed what one observes experimentally for convectional superconductors. 14.3.7. Experimental evidence of the BCS theory III: isotope effect Because the attraction is mediated by phonons in the BCS theory, the transition temperature should depend on the mass of nucleons. As shown above, for the BCS theory, Tc ∝ ϵD, where ϵD is the Debye energy. For an isotropic elastic medium, it is 6 π2 13 ϵD = ℏωD = ℏ v (14.9) VC -1/2 Here, VC is the volume of a unit cell and v is the sound velocity. The sound velocity is typically proportional to M , where M is the mass of the nucleons. For example, in Chapter 3, we calculated before the sound velocity for a 1D crystal, which has K v = a (14.10) M Here, a is the lattice spacing, K is the spring constant of the bond and M is the mass of the atom. -1/2 Therefore, we found that Tc ∝ ϵD ∝ v ∝ M , so the BCS theory predicts that α = 1/2 in the isotope effect, which is indeed what observed in experiments. 14.3.8. Experimental evidence of the BCS theory IV (the direct evidence): charge are carried by particles with charge -2 e, instead of -e Q: How to measure the charge of the carriers? A: the Aharonov–Bohm effect. Aharonove and Bohm told us that if we move a charged particle around a closed loop, the quantum wave function will pick up a phase Δϕ Δϕ = q ΦB /ℏ (14.11) where q is the charge of the particle and ΦB is the magnetic flux → → → → ΦB = B·ⅆ S = A·ⅆ r (14.12) S We know that in quantum physics, particles are waves and thus they have interference phenomenon.
    [Show full text]
  • Superconducting Shielding W.O
    Superconducting shielding W.O. Hamilton To cite this version: W.O. Hamilton. Superconducting shielding. Revue de Physique Appliquée, Société française de physique / EDP, 1970, 5 (1), pp.41-48. 10.1051/rphysap:019700050104100. jpa-00243373 HAL Id: jpa-00243373 https://hal.archives-ouvertes.fr/jpa-00243373 Submitted on 1 Jan 1970 HAL is a multi-disciplinary open access L’archive ouverte pluridisciplinaire HAL, est archive for the deposit and dissemination of sci- destinée au dépôt et à la diffusion de documents entific research documents, whether they are pub- scientifiques de niveau recherche, publiés ou non, lished or not. The documents may come from émanant des établissements d’enseignement et de teaching and research institutions in France or recherche français ou étrangers, des laboratoires abroad, or from public or private research centers. publics ou privés. REVUE DE PHYSIQUE APPLIQUÉE: TOME 5, FÉVRIER 1970, PAGE 41. SUPERCONDUCTING SHIELDING By W. O. HAMILTON, Stanford University, Department of Physics, Stanford, California (U.S.A.). Abstract. 2014 Superconducting shields offer the possibility of obtaining truly zero magnetic fields due to the phenomenon of flux quantization. They also offer excellent shielding from external time varying fields. Various techniques of superconducting shielding will be surveyed and recent results discussed. 1. Introduction. - Superconductivity has been a field of active research interest since its discovery in 1911. Many of the possible uses of superconducti- vity have been apparent from that time but it has been only recently that science and technology have progressed to the point that it has become absolutely necessary to use superconductors for important and practical measurements which are central to disciplines other than low temperature physics.
    [Show full text]
  • Stabilization of Phenomenon and Meaning
    European Journal for Philosophy of Science manuscript No. (will be inserted by the editor) Stabilization of Phenomenon and Meaning On the London & London episode as a historical case in philosophy of science Jan Potters Received: date / Accepted: date Abstract In recent years, the use of historical cases in philosophy of science has become a proper topic of reflection. In this article I will contribute to his research by means of a discussion of one very famous example of case-based philosophy of science, namely the debate on the London & London model of superconductivity between Cartwright, Su´arezand Shomar on the one hand, and French, Ladyman, Bueno and Da Costa on the other. This debate has been going on for years, without any satisfactory resolution. I will argue here that this is because both sides impose on the historical case a particular philosophical conception of scientific representation that does not do justice to the historical facts. Both sides assume, more specifically, that the case concerns the discovery of a representational connection between a given experimental insight { the Meissner effect { and the diamagnetic meaning of London and London's new equations of superconductivity. I will show, however, that at the time of the Londons' publication, neither the experimental insight nor the meaning of the new equations was established: both were open The author would like to acknowledge the Research Foundation { Flanders (FWO) as funding institution. Center for Philosophical Psychology, Department of Philosophy, University of Antwerp, Grote Kauwenberg 18, 2000 Antwerpen, Belgium E-mail: [email protected] 2 Jan Potters for discussion and they were stabilized only later.
    [Show full text]
  • How Alfven's Theorem Explains the Meissner Effect
    May 15, 2020 13:36 MPLB S0217984920503005 page 1 2nd Reading Modern Physics Letters B 2050300 (31 pages) © World Scientific Publishing Company DOI: 10.1142/S0217984920503005 How Alfven's theorem explains the Meissner effect J. E. Hirsch Department of Physics, University of California, San Diego, La Jolla, CA 92093-0319, USA Received 4 March 2020 Revised 13 April 2020 Accepted 17 April 2020 Published 16 May 2020 Alfven's theorem states that in a perfectly conducting fluid magnetic field lines move with the fluid without dissipation. When a metal becomes superconducting in the presence of a magnetic field, magnetic field lines move from the interior to the surface (Meissner effect) in a reversible way. This indicates that a perfectly conducting fluid is flowing outward. I point this out and show that this fluid carries neither charge nor mass, but carries effective mass. This implies that the effective mass of carriers is lowered when a system goes from the normal to the superconducting state, which agrees with the prediction of the unconventional theory of hole superconductivity and with optical experiments in some superconducting materials. The 60-year old conventional understanding of the Meissner effect ignores Alfven's theorem and for that reason I argue that it does not provide a valid understanding of real superconductors. Keywords: Alfven's theorem; Meissner effect; frozen field lines. Mod. Phys. Lett. B Downloaded from www.worldscientific.com PACS Number(s): 74.20.-z; 52.30.Cv 1. Introduction When a conducting fluid moves, magnetic field lines tend to move with the fluid, as a consequence of Faraday's law.1 If the fluid is perfectly conducting, the lines are \frozen" in the fluid.
    [Show full text]
  • On Magnetic Flux Trapping in Superconductors R
    TUOP08 Proceedings of LINAC2016, East Lansing, MI, USA ON MAGNETIC FLUX TRAPPING IN SUPERCONDUCTORS R. G. Eichhorn†, J. Hoke, Z. Mayle, CLASSE, Cornell University, Ithaca, USA Abstract Our research now indicates a third factor: the orientation Magnetic flux trapping on cool-down has become an im- of the magnetic field with respect to the superconductor portant factor in the performance of superconducting cavi- surface. ties. We have conducted systematic flux trapping experi- ments on samples to investigate the role of the orientation EXPERIMENTAL SET-UP of an ambient magnetic field relative to the niobium’s sur- To investigate the role of field orientation in flux trap- face. ping we designed a simple and flexible set-up. It consisted of a sample, clamped into position by a copper frame, two INTRODUCTION solenoids that could either be oriented parallel or orthogo- According to the perfect Meissner effect, a superconduc- nal to the sample, 4 flux gate sensors to measure magnetic tor is expected to expel all magnetic flux when it becomes field components (axial with respect to the sensor) and two superconducting. However, it is well known that supercon- cernox sensors to measure the temperature of the sample ducting cavities made from Niobium trap some of the mag- during the thermal cycle. Details of the set-up are shown in netic flux during the transitions to its superconducting state Fig. 1. while being exposed to an external magnetic field. The The solenoids consisted of wire coiled 25 times around trapped flux will result in normal conducting vortices, cylinders of stainless steel. Each solenoid had a diameter which add significantly to the total surface resistance.
    [Show full text]
  • Quantum Computing with Superconducting Devices
    6.763 Applied Superconductivity Lecture 1 Terry P. Orlando Dept. of Electrical Engineering MIT September 4, 2003 Outline • What is a Superconductor? • Discovery of Superconductivity • Meissner Effect • Type I Superconductors • Type II Superconductors • Theory of Superconductivity • Tunneling and the Josephson Effect • High-Temperature Supercondutors • Applications of Superconductors Massachusetts Institute of Technology What is a Superconductor? “A Superconductor has ZERO electrical resistance BELOW a certain critical temperature. Once set in motion, a persistent electric current will flow in the superconducting loop FOREVER without any power loss.” Magnetic Flux explusion A Superconductor EXCLUDES any magnetic fields that come near it. Massachusetts Institute of Technology How “Cool” are Superconductors? Below 77 Kelvin (-200 ºC): • Some Copper Oxide Ceramics superconduct Below 4 Kelvin (-270 ºC): • Some Pure Metals e.g. Lead, Mercury, Niobium superconduct Keeping at 77 K Keeping at 4K Keeping at 0 ºC Massachusetts Institute of Technology The Discovery of Superconductivity 1911 The Nobel Prize in Physics 1913 "for his investigations on the properties of matter at low temperatures which led, inter alia, to the production of liquid helium" Heike Kamerlingh Onnes the Netherlands Leiden University Leiden, the Netherlands b. 1853 d. 1926 •http://www.nobel.se/physics/laureates Discovery of Superconductivity “As has been said, the experiment left no doubt that, as far as accuracy of measurement went, the resistance disappeared. At the same time, however, something unexpected occurred. The disappearance did not take place gradually but (compare Fig. 17) abruptly. From 1/500 the resistance at 4.2oK drop to a millionth part. At the lowest temperature, 1.5oK, it could be established that the resistance had Resistance become less than a thousand-millionth part of that at normal temperature.
    [Show full text]
  • Elementary Properties of Superconductors
    Definition of Superconductivity http://www.wordiq.com/definition/Superconductivity Superconductivity SEARCH NOW Definition of Superconductivity Superconductivity is a phenomenon occurring in certain materials at low temperatures, characterised by the complete absence of electrical resistance and the damping of the interior magnetic field (the Meissner effect.) Superconductivity occurs in a wide variety of materials, including simple elements like tin and aluminium, various metallic alloys, some heavily-doped semiconductors, and certain ceramic compounds containing planes of copper and oxygen atoms. The latter class of compounds, known as the cuprates, are high-temperature superconductors. Superconductivity does not occur in noble metals like gold and silver, nor in ferromagnetic metals. In conventional superconductors, superconductivity is caused by a force of attraction between certain conduction electrons arising from the exchange of phonons, which causes the conduction electrons to exhibit a superfluid phase composed of correlated pairs of electrons. There also exists a class of materials, known as unconventional superconductors, that exhibit superconductivity but whose physical properties contradict the theory of conventional superconductors. In particular, the so-called high-temperature superconductors superconduct at temperatures much higher than should be possible according to the conventional theory (though still far below room temperature.) There is currently no complete theory of high-temperature superconductivity. Contents 1
    [Show full text]
  • Superconductivity: the Meissner Effect, Persistent Currents, and The
    Superconductivity: The Meissner Effect, Persistent Currents, and the Josephson Effects MIT Department of Physics (Dated: March 10, 2005) Several of the phenomena of superconductivity are observed in three experiments carried out in a liquid helium cryostat. The transition to the superconducting state of each of several bulk samples of Type I and II superconductors is observed in measurements of the exclusion of magnetic field (the Meisner effect) from samples as the temperature is gradually reduced by the flow of cold gas from boiling helium. The persistence of a current induced in a superconducting cylinder of lead is demonstrated by measurements of its magnetic field over a period of a day. The tunneling of Cooper pairs through an insulating junction between two superconductors (the DC Josephson effect) is demonstrated, and the magnitude of the fluxoid is measured by observation of the effect of a magnetic field on the Josephson current. 1. PREPARATORY QUESTIONS temperature. The liquid helium (liquefied at MIT in the Cryogenic Engineering Laboratory) is stored in a highly 1.How would you determine whether or notinsulated a sample Dewar flask. Certain precautions must be taken of some unknown material is capable ofin being its a manipulation.It is imperative that you read superconductor? the following section on Cryogenic Safety before proceeding with the experiment. 2.Calculate the loss rate of liquid helium from the dewar in L−1. d The density of liquid helium at 4.2K is 0.123− g3. cm At STP helium gas has a density of 0.178−1. g Data L for the measured2.1.
    [Show full text]